The Impact of Safe Moves on Perfectly Solving Domineering Boards - part 3: Theorems and Conjectures

Jos W. H. M. Uiterwijk*

*Corresponding author for this work

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This is the third and final article reporting on the impact of safe moves on perfectly solving Domineering boards. In the previous two articles (Uiterwijk, 2014b, 2014c) we gave an accurate analysis of obtainable safe moves in a Domineering game. Based on the results derived from a test set of all Domineering boards with sizes up to 30, new patterns were observed, suggesting general theorems. We prove two such theorems, extending previous theorems (Uiterwijk, 2014a, Lachmann, Moore, and Rapaport, 2002) considerably. The first theorem states that all 2k x n boards for n = 3, 5, 7, 9, and 11, and all 2k x13 boards with k >= 3, are a win for Vertical. The second theorem states that all m x 2k boards for m = 5, 9, and 13, all m x 2k boards for m = 3 and 7 with k >= 2, and all 11 x 2k boards with k >= 6, are a win for Horizontal. Moreover, we formulate two conjectures, namely that all (4k + 2) x 15 boards and, more generally, that all (4k + 2) x (4l + 3) boards for l
Original languageEnglish
Pages (from-to)207-213
Number of pages7
JournalICGA Journal
Issue number4
Publication statusPublished - Dec 2014

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